γεωμετρια α λυκειου βοηθημα 137-156
of 20
-
Upload
kiklades1209 -
Category
Documents
-
view
231 -
download
0
Transcript of γεωμετρια α λυκειου βοηθημα 137-156
-
8/11/2019 137-156
1/20
6 o
9o
10o
11
22
A B
O
x
B
-
8/11/2019 137-156
2/20
-
8/11/2019 137-156
3/20
9
.
i) ,
.
.. .
ii)
.
.. .
iii)
.
.. .
.
. :
( )1 x x K 2x 1= + =
KA
:( )2 2 2 2= + =
(1), (2) :
( )1 2 2x 2 2 x 2+ = + = + =
2 = .
.
.
A
A
x y
x1 2
-
8/11/2019 137-156
4/20
140.
.
.
. ,
.
.
( )
.
( > .
M). ,
< ( .
). 1
)
.
,
.
( )
12
= = .
( . ) x (
) ( ) x KB 2= . (1), (2)
x= .
,
,
.
BA .
, = + . .
M
B
T
T1
x
Z
-
8/11/2019 137-156
5/20
141.
.
BA ,
, = + ( ),
= .
1
.
,
1 2
=
. . 3 4
=
,
.
2
(,) .
.
, , 1 2
= = .
, ,
( ) 1= .
( = , 1= = , .
= ) 1 2
=
( ) 2= . ( ) 3= ,
(2), (3) = .
3
.
1
2 34
A
1 2
-
8/11/2019 137-156
6/20
142.
, : < . ,
.
. S= , S K<
S, < .
4
, . , ,
.
:
90=
. 90=
.
5
. .
.
= .
. .
:
( )1 1= ( )2 2= .
( )1 2 3= . (1), (2) = .
6
. ,
90= .
.
= = (
). = =
.
K
12
M
KS
B
K
-
8/11/2019 137-156
7/20
143.
7
.
= = .
( )A 1= ( )B 2= (
).
(1), (2) = .
( ) 3=
( ) 4=
(3), (4) : = .
8
. ,
.
, x
, x .
, x ,
, x .
E
H
x
y
-
8/11/2019 137-156
8/20
144.
.
( 430 - 347 . .)
- ,
-
.
.
.
.:
.
1,
2, . . . ,
,
.
-
.
()
.
1
(, ) = ,
.
, , , .
:
: .
1 : = ( )
2 : = ( )
3 : x= (. )
4 : x= ( )
:
x= , x=
= = ,
.
K
E
A
B
O
x
x
-
8/11/2019 137-156
9/20
145.
.
1
, (,) x
. ,
x, . :
. = + , . = 90 , . -
.
. = = .
+ = = + .
.1 2
= 1 2
= . x// :
2 2
180 90
2 2+ = + = + =
90= .
. ////, .
. .
2 2
+= ,
,
2
.
,
,2
.
2
( ) = = 90 = + . .
-
(////).
2 2
+= = ,
,
2
,
.
11
22
A B
O
x
-
8/11/2019 137-156
10/20
146.
3
. ,
> , (, ) .
(,) ,
.
= : = = .
= : = = . -
, . :
1
3= + = + + = + + = .
4
(, R) (, ) .
.
1
2 .
:
1 1 2 1
= = =
2 2
=
, .
1//
2.
5
.
. : //.
90=
1 2
90+ = .
( )
1 2
90 , + = = =
.
1 2
360+ + + + + = :
90 90 360 180 // + + + = + =
( -
).
6
xO, .
BA = 135 .
R 1
11
2
2
2
1
2
AK
B
1 2
-
8/11/2019 137-156
11/20
147.
,
x . 1 1 1 2
, = =
( = = ).
1 2 1 2
180 2 , 180 2= = = .
( )2 1 2 360 2 + = +
( ) ( ) 1 2 2 2 360 360 90 270 + = + = = .
1 2
135+ = 135= .
7
( > ) (,R).
, . :
. B = . = . ( ) = - > .
. = (
). = .
. = ,
2 2= = =
. ( )
2 2 90 180 2 2
2
= = = + =
= + + =
8
(,R) ,,,.
, , . .
.
2
=
2
= .
360
1802 2
++ = = = .
.
E
1
2O
AK
1
B
2
1
1
B HE
O
A
B
E
O
A
Z
-
8/11/2019 137-156
12/20
148.
9
(,R).
. . .
1
= , ,
1
= + = + .
= + ,
= .
10 (,) .
. .
.
90= ( ).
1 1
= , .
= .
2 1
= , 1 1
=
= .
2
= = .
11
(,) .
.
AA , .
,
.
= = .
= .
12
(, ) (, ) .
(, ) (, ).
//=.
AO
B
1
1
12
E
O
-
8/11/2019 137-156
13/20
149.
.
90 90
= + =
2 2 180 180 // + = + = .
= = .
. //=.
13
( = ) (,). ,
, ,
. .
AB A= = , 1 2
= (1) ,
.
.
.
14
(,), .
. :
.
. = /2 = /2.
. , = = = .
= ( B )
90+ = , 90+ = .
. .
. , //.
, //. -
:
2= =
2= = .
15
, . -
= . ,
. :
. = . //.
K A
B
O
BE
K
1 2
A
-
8/11/2019 137-156
14/20
150.
= , -
. 1 2
= = .
,
, (
1 2
= ). = , = ,
,.
. = ( ).
. ,
, .
//.
16
.
, : = .
90= . :1 1
= + ,( ).
1 21
2=
1 11
2=
(
), :
( ) 02 1 1 21 1 1 1 1
90 452 2 2 2 2
= + = + = = =
.
= .
O BA
Z K
H
E
1 2
11
1
2
OB
E
A
-
8/11/2019 137-156
15/20
151.
.
1.
(,). ,
, .
EOB 3O= .
2. .
30= . -
, . = .
3. (, R) (, )
. ,
, -
,
.
4.
.
,
( ).
= .
5.
. , , .
.
6.
, .
,
180 - .
EZ
EZ
-
8/11/2019 137-156
16/20
152.
7. (, R) (, ) R > , -
. (, R)
(, ) .
. (, )
, (,
).
8. (, R) (, )
. , (,
) (, R) . (, R), -
.
9.
.
,
.
10. (, R) (,)
. -
. :
.
. -
. .
.
11. (,R)
120 .
.
-
.
AO B K
E
A R K
B
O
E
OA K
B
KE
BA
B
E
O
A
-
8/11/2019 137-156
17/20
153.
12. , , (, R).
. .
13. -
.
, ,
.
14.
. .
.
15.
- 90= .
.
16. . .
x ,
, Bx .
= .
B
M
O
A
K
A
B
K
AE
B
AO
B
x
Z
M
-
8/11/2019 137-156
18/20
154.
17. (,) .
= = . :
. = .
